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Stranded migrants scramble up Greek cliff face
Further east, a total of 16 bodies have been recovered by rescuers near the island of Lesbos after a dinghy carrying around 40 people got into difficulty on Wednesday night.
Nine people were rescued and around 15 remained missing.
Most migrants reaching Greece travel from neighbouring Turkey, but smugglers have changed routes in recent months to avoid heavily patrolled waters around Greek islands near the Turkish coastline.
Greece has toughened its migration policy in recent years and regularly carries out interceptions of boats at sea – a move which has been criticised by some human rights groups.
The country has repeatedly blamed Turkey for not taking sufficient measures to stop migrants from making the dangerous journey.
Kythira is some 250 miles (450km) west of Turkey and part of a route often used by smugglers to bypass Greece and head directly to Italy.